Bujutsu 武術 is a generic Japanese term associated to Koryu Bu or warring ways

Aiki 合気 and methods of warring ways are in conflict with each other from both a technical and ideological perspective so, to use "aikibujutsu" as a name for something martially orientated is fucking stupid.

Ueshiba Morihei used the term Aikibudo - Budo 武道 being a term which whilst interchangeable with bujutsu, has far less warring connotation to that of the jutsu version.

The ONLY martial system to have coined the term Aiki as part of it's formal Ryu name was Dai-to Ryu Aikijujutsu 大東流合気柔術 and this was long after the Meiji Restoration and followed a meeting between Deguchi Onisaburo and Takeda Sokaku.

First off, for info on aikibujutsu, see earlier comments on this thread, and try using Google. I assume you know how to use the interwebs since you made it this far. Is there a reason for the essay? It's not like your jujuitsu teacher is going to fail you or give you a crappy grade and if this is for a belt or something you might want to find a more serious gym. Slightly off-topic, how old are you? Because I know at some schools they have silly project type stuff for people in kids' classes; but, I've never heard of having to write an essay or do any sort of project for an adult class in any martial art.